Polynomial Iterative Learning Control (ILC) Tracking Control Design for Uncertain Repetitive Continuous-Time Linear Systems Applied to an Active Suspension of a Car Seat †
Abstract
:1. Introduction
2. Problem Statement and Preliminaries
Stability along the Pass for 2D Repetitive Systems
- (i)
- A is stable and
- (ii)
- There exists a positive symmetric matrix X such that the following LMI is feasible:
3. Main Results
3.1. Control Objective
- (A1) The desired output is given a prior over the same time duration; it is assumed that the initial resetting condition is satisfied, i.e., .
- (A2) The initial state remains the same at each iteration, i.e., . For any given assumption A1 and A2, one desirable objective in ILC is that converges monotonically to when k tends to infinity for all t within the time interval since it can guarantee reasonable transients during the learning process [3]. In the sense of the, norm, this objective can be transformed by considering the index [8].Obviously, the norm error can be guaranteed to converge monotonically along the iteration axis k if holds for any .
3.2. ILC Tracking Control
3.3. ILC Tracking Control Using D-Stability along the Pass
3.4. D-Stability along the Pass for Continuous Linear Repetitive Process
3.5. Polynomial ILC Control
- Introducing a novel polynomial-based approach to iterative learning control, which offers a flexible and intuitive framework for defining desired trajectories.
- Advancing existing techniques by providing a systematic methodology for designing and optimizing polynomial-based control laws for repetitive systems.
- Demonstrating improved tracking performance and robustness compared to traditional ILC methods, particularly in applications with complex and time-varying dynamics. Overall, Poly-ILC represents a significant advancement in the field of iterative learning control, offering a powerful and versatile approach for achieving accurate and reliable tracking in repetitive systems.
4. Uncertain LRP Systems
4.1. Problem Formulation
4.2. Poly-Quadratic Stability
5. Numerical Examples
5.1. Comparison between D-ILC Tracking Control and D-Poly-ILC Tracking Control
5.1.1. ILC Controller for Desired Performances
- Overshoot .
- Setting time at .
5.1.2. Tracking Error Convergence
5.1.3. Discussion
5.2. Uncertain Case
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Parameters | Approaches | Learning Gains |
---|---|---|
Theorem 6 | ||
Theorem 7 | ||
Parameters | Approach | Learning Gains |
---|---|---|
Theorem 7 | ||
0.36 | 0.9 | 0.9 | 0.3503 |
0.25 | 0.9 | 0.9 | 0.232 |
0.15 | 0.9 | 0.9 | 0.148 |
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Attia, S.B.; Alzahrani, S.; Alhuwaimel, S.; Salhi, S.; Ouerfelli, H.E. Polynomial Iterative Learning Control (ILC) Tracking Control Design for Uncertain Repetitive Continuous-Time Linear Systems Applied to an Active Suspension of a Car Seat. Mathematics 2024, 12, 2573. https://doi.org/10.3390/math12162573
Attia SB, Alzahrani S, Alhuwaimel S, Salhi S, Ouerfelli HE. Polynomial Iterative Learning Control (ILC) Tracking Control Design for Uncertain Repetitive Continuous-Time Linear Systems Applied to an Active Suspension of a Car Seat. Mathematics. 2024; 12(16):2573. https://doi.org/10.3390/math12162573
Chicago/Turabian StyleAttia, Selma Ben, Sultan Alzahrani, Saad Alhuwaimel, Salah Salhi, and Houssem Eddine Ouerfelli. 2024. "Polynomial Iterative Learning Control (ILC) Tracking Control Design for Uncertain Repetitive Continuous-Time Linear Systems Applied to an Active Suspension of a Car Seat" Mathematics 12, no. 16: 2573. https://doi.org/10.3390/math12162573